My puppy has never peed outside

-Have you tried bringing a pad that she already peed on or some of her poop outside? If she smells her own there, she may make the connection.

-I don't know if it's possible in your situation, but I've actually heard of some people just staying outside with their puppy the whole day- eventually she'll need to go, which gives you the opportunity to reinforce heavily.

-And since you said she went right after, I realize in your home you cannot take her out in time if you realize she's about to, but there are 2 potential solutions: a) once she goes upon you taking her inside, take her (and the dirty potty pad) outside, to at least build an association with going outside. b) if she makes a habit of this, take her inside for just a moment, then go right back out.

-Another tip is to not go somewhere with so much to smell- even if it's other dog's poop. You want the area where you are teaching her to go potty to be boring. It may be that she's too stimulated and distracted while outside, and so she forgets that she needs to go potty. Then she comes inside, is no longer so distracted, and so she "remembers". Go to whatever place is the most boring (from the dog's perspective, not the human's- sometimes this is challenging) and stay there- don't make yourself to interesting by asking her to potty. Don't let your dog wander around too much, but also don't keep her right by your side, as she may be "potty shy". Stay there for as long as it takes for her to become bored- it's quite possible that she will potty then. Don't let her play or sniff outside until after she's gone potty.

-Also- you said you have her going in her crate? Does she have a bed or some other clean space where she can be? It's possible that having her potty spot in her "den" is confusing her, because it's almost saying that there aren't rules about where to potty.

-Here's a link to a discussion on another forum:
Potty training nightmare
you may find it helpful, although it's a somewhat different situation